Mind the last spike — firing rate models for mesoscopic populations of spiking neurons

• Published in: Current opinion in neurobiology 2019-10, Vol.58, p.155-166
• Main Authors: Schwalger, Tilo, Chizhov, Anton V
• Format: Article
• Language: English
• Subjects: Action Potentials; Biophysics; Computer Simulation; Models, Neurological; Neurons
• ISSN: 0959-4388; 1873-6882
• DOI: 10.1016/j.conb.2019.08.003

•Generalized integrate-and-fire (GIF) models permit efficient extraction of point neuron parameters, which reproduce the spiking behavior of multiple cell types and are available from a public database.•Populations of GIF or conductance-based neuron models can be described by a single state variable — the “time since the last spike” — enabling efficient refractory density methods.•Refractory density model accurately captures transient dynamics and finite-size fluctuations of mesoscopic activities of spiking neuron populations.•Next-generation firing-rate models for finite-size populations of spiking neurons arise from a low-dimensional reduction of the refractory density equation. The dominant modeling framework for understanding cortical computations are heuristic firing rate models. Despite their success, these models fall short to capture spike synchronization effects, to link to biophysical parameters and to describe finite-size fluctuations. In this opinion article, we propose that the refractory density method (RDM), also known as age-structured population dynamics or quasi-renewal theory, yields a powerful theoretical framework to build rate-based models for mesoscopic neural populations from realistic neuron dynamics at the microscopic level. We review recent advances achieved by the RDM to obtain efficient population density equations for networks of generalized integrate-and-fire (GIF) neurons — a class of neuron models that has been successfully fitted to various cell types. The theory not only predicts the nonstationary dynamics of large populations of neurons but also permits an extension to finite-size populations and a systematic reduction to low-dimensional rate dynamics. The new types of rate models will allow a re-examination of models of cortical computations under biological constraints.